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math.PR2025
Concentration and moment inequalities for sums of independent heavy-tailed random matrices
Moritz Jirak, Stanislav Minsker, Yiqiu Shen +1
We prove Fuk-Nagaev and Rosenthal-type inequalities for sums of independent random matrices, focusing on the situation when the norms of the matrices possess finite moments of only…
math.PR2025
Weak dependence and optimal quantitative self-normalized central limit theorems
Moritz Jirak
Consider a stationary, weakly dependent sequence of random variables. Given only mild conditions, allowing for polynomial decay of the autocovariance function, we show a Berry-Esse…
math.PR2024
Quantitative limit theorems and bootstrap approximations for empirical spectral projectors
Moritz Jirak, Martin Wahl
Given finite i.i.d.~samples in a Hilbert space with zero mean and trace-class covariance operator , the problem of recovering the spectral projectors of naturally arises i…